For the BBQ sauce: Preheat a medium saucepot with EVOO over medium heat. Sauté onion and garlic until soft and slightly caramelized; season with salt and ground pepper. Add the ketchup, mustard, brown sugar, maple syrup, vinegar, Worcestershire sauce and bourbon. Simmer over medium-low heat, stirring occasionally, about 20 minutes until slightly thickened.
For Pulled Chicken BBQ: Pull the meat from the chicken discarding the skin and bones. Place the meat into the large skillet with BBQ sauce; add a splash of chicken stock or water. Serve on buns or lettuce wraps with toppings of choice and some Cabbage Apple Slaw.